Übungen am 6.12.2001

Übungen zu "Computergestütztes symbolisches Rechnen" im Wintersemester 2001/02, Institut für Informatik der Universität München

Aufgabe 8

f = x^3 - x^2  y - x^2  z + x

g1 = x^2  y - z

g2 = x y - 1

Teilaufgabe 1

o1 = 
      PolynomialReduce[f, {g1, g2}, {x, y, z}, 
        MonomialOrder -> DegreeLexicographic]

r1 = Last[%]

o2 = 
      PolynomialReduce[f, {g2, g1}, {x, y, z}, 
        MonomialOrder -> DegreeLexicographic]

r2 = Last[%]

Expand[f - x^3 - g1*(-1)]

Expand[f - x^3 - g2*(-x)]

Teilaufgabe 2

r = r1 - r2

Expand[Part[o2, 1, 1]*g2 - Part[o1, 1, 1]*g1]

Teilaufgabe 3

PolynomialReduce[r, {g1, g2}, {x, y, z}, 
      MonomialOrder -> DegreeLexicographic]

Teilaufgabe 4

h = Expand[y r - g2]

PolynomialReduce[h, {g1, g2}, {x, y, z}, 
      MonomialOrder -> DegreeLexicographic]

Aufgabe 9

g1 = x^4  y^2 - z

g2 = x^3  y^3 - 1

g3 = x^2  y^4 - 2  z

f1 = Expand[y g1 - x g2]

red[f_] := 
      PolynomialReduce[f, {g1, g2, g3}, {x, y, z}, 
        MonomialOrder -> DegreeLexicographic]

red[f1]

f2 = Expand[y g2 - x g3]

red[f2]